All the people are not the same so there are many variations in their way of thinking. KYC seems normal to some but dangerous to others. Overall casino gambling platform can benefit a gambler in several ways. In particular, it is possible to get proper solutions for withdrawal and account related problems. Now a days a gambler's personal information is stored securely in all the reputable casinos or gambling platforms. A gambler can be involved in various types of crimes. Once KYC is completed, casino gambling platforms have information of the customers so that no one can commit crimes.
To be honest, gambling site will not ask you KYC if there was no regulation to force those site to comply with AML regulation. The gambling site only needs your money but they don't care so much with our identity. The only problem if regulators have been making it as standard for gamblign site to make sure it will be far from dealing with the money laundering. That's why sometime the site was asking for KYC. As long as it stored securely and i think that people have no problem with it.
The only problem if data gets leaked and this gonna be a problem. It's all about how to comply with the regulation that's followed by the gambling provider.